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   "source": [
    "# Assignment 2: Markov Decision Processes\n",
    "\n",
    "\n",
    "## Homework Instructions\n",
    "All your answers should be written in this notebook.  You shouldn't need to write or modify any other files.\n",
    "Look for four instances of \"YOUR CODE HERE\"--those are the only parts of the code you need to write. To grade your homework, we will check whether the printouts immediately following your code match up with the results we got. The portions used for grading are highlighted in yellow. (However, note that the yellow highlighting does not show up when github renders this file.)\n",
    "\n",
    "To submit your homework, send an email to <berkeleydeeprlcourse@gmail.com> with the subject line \"Deep RL Assignment 2\" and two attachments:\n",
    "1. This `ipynb` file\n",
    "2. A pdf version of this file (To make the pdf, do `File - Print Preview`)\n",
    "\n",
    "The homework is due Febrary 22nd, 11:59 pm.\n",
    "\n",
    "--------------------------"
   ]
  },
  {
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   "source": [
    "## Introduction\n",
    "\n",
    "This assignment will review the two classic methods for solving Markov Decision Processes (MDPs) with finite state and action spaces.\n",
    "We will implement value iteration (VI) and policy iteration (PI) for a finite MDP, both of which find the optimal policy in a finite number of iterations.\n",
    "\n",
    "The experiments here will use the Frozen Lake environment, a simple gridworld MDP that is taken from `gym` and slightly modified for this assignment. In this MDP, the agent must navigate from the start state to the goal state on a 4x4 grid, with stochastic transitions."
   ]
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     "text": [
      "\n",
      "    Winter is here. You and your friends were tossing around a frisbee at the park\n",
      "    when you made a wild throw that left the frisbee out in the middle of the lake.\n",
      "    The water is mostly frozen, but there are a few holes where the ice has melted.\n",
      "    If you step into one of those holes, you'll fall into the freezing water.\n",
      "    At this time, there's an international frisbee shortage, so it's absolutely imperative that\n",
      "    you navigate across the lake and retrieve the disc.\n",
      "    However, the ice is slippery, so you won't always move in the direction you intend.\n",
      "    The surface is described using a grid like the following\n",
      "\n",
      "        SFFF\n",
      "        FHFH\n",
      "        FFFH\n",
      "        HFFG\n",
      "\n",
      "    S : starting point, safe\n",
      "    F : frozen surface, safe\n",
      "    H : hole, fall to your doom\n",
      "    G : goal, where the frisbee is located\n",
      "\n",
      "    The episode ends when you reach the goal or fall in a hole.\n",
      "    You receive a reward of 1 if you reach the goal, and zero otherwise.\n",
      "\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "from frozen_lake import FrozenLakeEnv\n",
    "env = FrozenLakeEnv()\n",
    "print(env.__doc__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at what a random episode looks like."
   ]
  },
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     "text": [
      "\n",
      "\u001b[41mS\u001b[0mFFF\n",
      "FHFH\n",
      "FFFH\n",
      "HFFG\n",
      "  (Down)\n",
      "S\u001b[41mF\u001b[0mFF\n",
      "FHFH\n",
      "FFFH\n",
      "HFFG\n",
      "  (Down)\n",
      "SFFF\n",
      "F\u001b[41mH\u001b[0mFH\n",
      "FFFH\n",
      "HFFG\n"
     ]
    }
   ],
   "source": [
    "# Some basic imports and setup\n",
    "import numpy as np, numpy.random as nr, gym\n",
    "np.set_printoptions(precision=3)\n",
    "def begin_grading(): print(\"\\x1b[43m\")\n",
    "def end_grading(): print(\"\\x1b[0m\")\n",
    "\n",
    "# Seed RNGs so you get the same printouts as me\n",
    "env.seed(0); from gym.spaces import prng; prng.seed(10)\n",
    "# Generate the episode\n",
    "env.reset()\n",
    "for t in range(100):\n",
    "    env.render()\n",
    "    a = env.action_space.sample()\n",
    "    ob, rew, done, _ = env.step(a)\n",
    "    if done:\n",
    "        break\n",
    "assert done\n",
    "env.render();"
   ]
  },
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   "source": [
    "In the episode above, the agent falls into a hole after two timesteps. Also note the stochasticity--on the first step, the DOWN action is selected, but the agent moves to the right.\n",
    "\n",
    "We extract the relevant information from the gym Env into the MDP class below.\n",
    "The `env` object won't be used any further, we'll just use the `mdp` object."
   ]
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     "text": [
      "mdp.P is a two-level dict where the first key is the state and the second key is the action.\n",
      "The 2D grid cells are associated with indices [0, 1, 2, ..., 15] from left to right and top to down, as in\n",
      "[[ 0  1  2  3]\n",
      " [ 4  5  6  7]\n",
      " [ 8  9 10 11]\n",
      " [12 13 14 15]]\n",
      "mdp.P[state][action] is a list of tuples (probability, nextstate, reward).\n",
      "\n",
      "For example, state 0 is the initial state, and the transition information for s=0, a=0 is \n",
      "P[0][0] = [(0.1, 0, 0.0), (0.8, 0, 0.0), (0.1, 4, 0.0)] \n",
      "\n",
      "As another example, state 5 corresponds to a hole in the ice, which transitions to itself with probability 1 and reward 0.\n",
      "P[5][0] = [(1.0, 5, 0)] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "class MDP(object):\n",
    "    def __init__(self, P, nS, nA, desc=None):\n",
    "        self.P = P # state transition and reward probabilities, explained below\n",
    "        self.nS = nS # number of states\n",
    "        self.nA = nA # number of actions\n",
    "        self.desc = desc # 2D array specifying what each grid cell means (used for plotting)\n",
    "mdp = MDP( {s : {a : [tup[:3] for tup in tups] for (a, tups) in a2d.items()} for (s, a2d) in env.P.items()}, env.nS, env.nA, env.desc)\n",
    "\n",
    "\n",
    "print(\"mdp.P is a two-level dict where the first key is the state and the second key is the action.\")\n",
    "print(\"The 2D grid cells are associated with indices [0, 1, 2, ..., 15] from left to right and top to down, as in\")\n",
    "print(np.arange(16).reshape(4,4))\n",
    "print(\"mdp.P[state][action] is a list of tuples (probability, nextstate, reward).\\n\")\n",
    "print(\"For example, state 0 is the initial state, and the transition information for s=0, a=0 is \\nP[0][0] =\", mdp.P[0][0], \"\\n\")\n",
    "print(\"As another example, state 5 corresponds to a hole in the ice, which transitions to itself with probability 1 and reward 0.\")\n",
    "print(\"P[5][0] =\", mdp.P[5][0], '\\n')"
   ]
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   "source": [
    "## Part 1: Value Iteration"
   ]
  },
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   "source": [
    "### Problem 1: implement value iteration\n",
    "In this problem, you'll implement value iteration, which has the following pseudocode:\n",
    "\n",
    "---\n",
    "Initialize $V^{(0)}(s)=0$, for all $s$\n",
    "\n",
    "For $i=0, 1, 2, \\dots$\n",
    "- $V^{(i+1)}(s) = \\max_a \\sum_{s'} P(s,a,s') [ R(s,a,s') + \\gamma V^{(i)}(s')]$, for all $s$\n",
    "\n",
    "---\n",
    "\n",
    "We additionally define the sequence of greedy policies $\\pi^{(0)}, \\pi^{(1)}, \\dots, \\pi^{(n-1)}$, where\n",
    "$$\\pi^{(i)}(s) = \\arg \\max_a \\sum_{s'} P(s,a,s') [ R(s,a,s') + \\gamma V^{(i)}(s')]$$\n",
    "\n",
    "Your code will return two lists: $[V^{(0)}, V^{(1)}, \\dots, V^{(n)}]$ and $[\\pi^{(0)}, \\pi^{(1)}, \\dots, \\pi^{(n-1)}]$\n",
    "\n",
    "To ensure that you get the same policies as the reference solution, choose the lower-index action to break ties in $\\arg \\max_a$. This is done automatically by np.argmax. This will only affect the \"# chg actions\" printout below--it won't affect the values computed.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "Warning: make a copy of your value function each iteration and use that copy for the update--don't update your value function in place. \n",
    "Updating in-place is also a valid algorithm, sometimes called Gauss-Seidel value iteration or asynchronous value iteration, but it will cause you to get different results than me.\n",
    "</div>"
   ]
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     "text": [
      "\u001b[43m\n",
      "Iteration | max|V-Vprev| | # chg actions | V[0]\n",
      "----------+--------------+---------------+---------\n",
      "   0      | 0.80000      |  N/A          | 0.000\n",
      "   1      | 0.60800      |    2          | 0.000\n",
      "   2      | 0.51984      |    2          | 0.000\n",
      "   3      | 0.39508      |    2          | 0.000\n",
      "   4      | 0.30026      |    2          | 0.000\n",
      "   5      | 0.25355      |    1          | 0.254\n",
      "   6      | 0.10478      |    0          | 0.345\n",
      "   7      | 0.09657      |    0          | 0.442\n",
      "   8      | 0.03656      |    0          | 0.478\n",
      "   9      | 0.02772      |    0          | 0.506\n",
      "  10      | 0.01111      |    0          | 0.517\n",
      "  11      | 0.00735      |    0          | 0.524\n",
      "  12      | 0.00310      |    0          | 0.527\n",
      "  13      | 0.00190      |    0          | 0.529\n",
      "  14      | 0.00083      |    0          | 0.530\n",
      "  15      | 0.00049      |    0          | 0.531\n",
      "  16      | 0.00022      |    0          | 0.531\n",
      "  17      | 0.00013      |    0          | 0.531\n",
      "  18      | 0.00006      |    0          | 0.531\n",
      "  19      | 0.00003      |    0          | 0.531\n",
      "\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "def value_iteration(mdp, gamma, nIt):\n",
    "    \"\"\"\n",
    "    Inputs:\n",
    "        mdp: MDP\n",
    "        gamma: discount factor\n",
    "        nIt: number of iterations, corresponding to n above\n",
    "    Outputs:\n",
    "        (value_functions, policies)\n",
    "        \n",
    "    len(value_functions) == nIt+1 and len(policies) == n\n",
    "    \"\"\"\n",
    "    print(\"Iteration | max|V-Vprev| | # chg actions | V[0]\")\n",
    "    print(\"----------+--------------+---------------+---------\")\n",
    "    Vs = [np.zeros(mdp.nS)] # list of value functions contains the initial value function V^{(0)}, which is zero\n",
    "    pis = []\n",
    "    for it in range(nIt):\n",
    "        oldpi = pis[-1] if len(pis) > 0 else None # \\pi^{(it)} = Greedy[V^{(it-1)}]. Just used for printout\n",
    "        Vprev = Vs[-1] # V^{(it)}\n",
    "        # YOUR CODE HERE\n",
    "        # Your code should define the following two variables\n",
    "        # pi: greedy policy for Vprev, \n",
    "        #     corresponding to the math above: \\pi^{(it)} = Greedy[V^{(it)}]\n",
    "        #     numpy array of ints\n",
    "        # V: bellman backup on Vprev\n",
    "        #     corresponding to the math above: V^{(it+1)} = T[V^{(it)}]\n",
    "        #     numpy array of floats\n",
    "        max_diff = np.abs(V - Vprev).max()\n",
    "        nChgActions=\"N/A\" if oldpi is None else (pi != oldpi).sum()\n",
    "        print(\"%4i      | %6.5f      | %4s          | %5.3f\"%(it, max_diff, nChgActions, V[0]))\n",
    "        Vs.append(V)\n",
    "        pis.append(pi)\n",
    "    return Vs, pis\n",
    "\n",
    "GAMMA=0.95 # we'll be using this same value in subsequent problems\n",
    "begin_grading()\n",
    "Vs_VI, pis_VI = value_iteration(mdp, gamma=GAMMA, nIt=20)\n",
    "end_grading()\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we've illustrated the progress of value iteration. Your optimal actions are shown by arrows.\n",
    "At the bottom, the value of the different states are plotted."
   ]
  },
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   "cell_type": "code",
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    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddd3128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1124543c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1124544a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1124e4278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11266e390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1126fb710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1127a4208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1127a40f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1128b54a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112940e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JKc89B0uXQsuWMGUKXHedEQSCIAh1lAULFrBgwYJKaXl5eUErXwWyVMY53FAE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\nJEgQQgghRL/+P7dGer07MS3qAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddccfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "for (V, pi) in zip(Vs_VI[:10], pis_VI[:10]):\n",
    "    plt.figure(figsize=(3,3))\n",
    "    plt.imshow(V.reshape(4,4), cmap='gray', interpolation='none', clim=(0,1))\n",
    "    ax = plt.gca()\n",
    "    ax.set_xticks(np.arange(4)-.5)\n",
    "    ax.set_yticks(np.arange(4)-.5)\n",
    "    ax.set_xticklabels([])\n",
    "    ax.set_yticklabels([])\n",
    "    Y, X = np.mgrid[0:4, 0:4]\n",
    "    a2uv = {0: (-1, 0), 1:(0, -1), 2:(1,0), 3:(-1, 0)}\n",
    "    Pi = pi.reshape(4,4)\n",
    "    for y in range(4):\n",
    "        for x in range(4):\n",
    "            a = Pi[y, x]\n",
    "            u, v = a2uv[a]\n",
    "            plt.arrow(x, y,u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) \n",
    "            plt.text(x, y, str(env.desc[y,x].item().decode()),\n",
    "                     color='g', size=12,  verticalalignment='center',\n",
    "                     horizontalalignment='center', fontweight='bold')\n",
    "    plt.grid(color='b', lw=2, ls='-')\n",
    "plt.figure()\n",
    "plt.plot(Vs_VI)\n",
    "plt.title(\"Values of different states\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 2: construct an MDP where value iteration takes a long time to converge\n",
    "\n",
    "When we ran value iteration on the frozen lake problem, the last iteration where an action changed was iteration 6--i.e., value iteration computed the optimal policy at iteration 6.\n",
    "Are there any guarantees regarding how many iterations it'll take value iteration to compute the optimal policy?\n",
    "There are no such guarantees without additional assumptions--we can construct the MDP in such a way that the greedy policy will change after arbitrarily many iterations.\n",
    "\n",
    "Your task: define an MDP with at most 3 states and 2 actions, such that when you run value iteration, the optimal action changes at iteration >= 50. Use discount=0.95. (However, note that the discount doesn't matter here--you can construct an appropriate MDP with any discount.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[43m\n",
      "Iteration | max|V-Vprev| | # chg actions | V[0]\n",
      "----------+--------------+---------------+---------\n",
      "   0      | 1.00000      |  N/A          | 1.000\n",
      "   1      | 0.05441      |    0          | 1.000\n",
      "   2      | 0.05169      |    0          | 1.000\n",
      "   3      | 0.04910      |    0          | 1.000\n",
      "   4      | 0.04665      |    0          | 1.000\n",
      "   5      | 0.04431      |    0          | 1.000\n",
      "   6      | 0.04210      |    0          | 1.000\n",
      "   7      | 0.03999      |    0          | 1.000\n",
      "   8      | 0.03799      |    0          | 1.000\n",
      "   9      | 0.03609      |    0          | 1.000\n",
      "  10      | 0.03429      |    0          | 1.000\n",
      "  11      | 0.03258      |    0          | 1.000\n",
      "  12      | 0.03095      |    0          | 1.000\n",
      "  13      | 0.02940      |    0          | 1.000\n",
      "  14      | 0.02793      |    0          | 1.000\n",
      "  15      | 0.02653      |    0          | 1.000\n",
      "  16      | 0.02521      |    0          | 1.000\n",
      "  17      | 0.02395      |    0          | 1.000\n",
      "  18      | 0.02275      |    0          | 1.000\n",
      "  19      | 0.02161      |    0          | 1.000\n",
      "  20      | 0.02053      |    0          | 1.000\n",
      "  21      | 0.01950      |    0          | 1.000\n",
      "  22      | 0.01853      |    0          | 1.000\n",
      "  23      | 0.01760      |    0          | 1.000\n",
      "  24      | 0.01672      |    0          | 1.000\n",
      "  25      | 0.01589      |    0          | 1.000\n",
      "  26      | 0.01509      |    0          | 1.000\n",
      "  27      | 0.01434      |    0          | 1.000\n",
      "  28      | 0.01362      |    0          | 1.000\n",
      "  29      | 0.01294      |    0          | 1.000\n",
      "  30      | 0.01229      |    0          | 1.000\n",
      "  31      | 0.01168      |    0          | 1.000\n",
      "  32      | 0.01109      |    0          | 1.000\n",
      "  33      | 0.01054      |    0          | 1.000\n",
      "  34      | 0.01001      |    0          | 1.000\n",
      "  35      | 0.00951      |    0          | 1.000\n",
      "  36      | 0.00904      |    0          | 1.000\n",
      "  37      | 0.00858      |    0          | 1.000\n",
      "  38      | 0.00816      |    0          | 1.000\n",
      "  39      | 0.00775      |    0          | 1.000\n",
      "  40      | 0.00736      |    0          | 1.000\n",
      "  41      | 0.00699      |    0          | 1.000\n",
      "  42      | 0.00664      |    0          | 1.000\n",
      "  43      | 0.00631      |    0          | 1.000\n",
      "  44      | 0.00599      |    0          | 1.000\n",
      "  45      | 0.00569      |    0          | 1.000\n",
      "  46      | 0.00541      |    0          | 1.000\n",
      "  47      | 0.00514      |    0          | 1.000\n",
      "  48      | 0.00488      |    0          | 1.000\n",
      "  49      | 0.00464      |    0          | 1.000\n",
      "  50      | 0.00441      |    1          | 1.004\n",
      "\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "chg_iter = 50\n",
    "# YOUR CODE HERE\n",
    "# Your code will need to define an MDP (mymdp)\n",
    "# like the frozen lake MDP defined above\n",
    "begin_grading()\n",
    "Vs, pis = value_iteration(mymdp, gamma=GAMMA, nIt=chg_iter+1)\n",
    "end_grading()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3: Policy Iteration\n",
    "\n",
    "The next task is to implement exact policy iteration (PI), which has the following pseudocode:\n",
    "\n",
    "---\n",
    "Initialize $\\pi_0$\n",
    "\n",
    "For $n=0, 1, 2, \\dots$\n",
    "- Compute the state-value function $V^{\\pi_{n}}$\n",
    "- Using $V^{\\pi_{n}}$, compute the state-action-value function $Q^{\\pi_{n}}$\n",
    "- Compute new policy $\\pi_{n+1}(s) = \\operatorname*{argmax}_a Q^{\\pi_{n}}(s,a)$\n",
    "---\n",
    "\n",
    "Below, you'll implement the first and second steps of the loop.\n",
    "\n",
    "### Problem 3a: state value function\n",
    "\n",
    "You'll write a function called `compute_vpi` that computes the state-value function $V^{\\pi}$ for an arbitrary policy $\\pi$.\n",
    "Recall that $V^{\\pi}$ satisfies the following linear equation:\n",
    "$$V^{\\pi}(s) = \\sum_{s'} P(s,\\pi(s),s')[ R(s,\\pi(s),s') + \\gamma V^{\\pi}(s')]$$\n",
    "You'll have to solve a linear system in your code. (Find an exact solution, e.g., with `np.linalg.solve`.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def compute_vpi(pi, mdp, gamma):\n",
    "    # YOUR CODE HERE\n",
    "    return V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compute the value of an arbitrarily-chosen policy. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[43m\n",
      "[  1.638e-02   2.357e-02   2.317e-01   2.433e-02   1.656e-02  -0.000e+00\n",
      "   2.989e-01   0.000e+00   1.972e-02   1.879e-01   3.934e-01   0.000e+00\n",
      "  -3.581e-17   1.956e-01   4.941e-01   0.000e+00]\n",
      "\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "begin_grading()\n",
    "print(compute_vpi(np.ones(16), mdp, gamma=GAMMA))\n",
    "end_grading()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a sanity check, if we run `compute_vpi` on the solution from our previous value iteration run, we should get approximately (but not exactly) the same values produced by value iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From compute_vpi [ 0.531  0.471  0.56   0.471  0.574 -0.     0.62   0.     0.683  0.827\n",
      "  0.815  0.     0.     0.901  0.97   0.   ]\n",
      "From value iteration [ 0.53   0.47   0.56   0.47   0.573  0.     0.62   0.     0.683  0.827\n",
      "  0.815  0.     0.     0.901  0.97   0.   ]\n",
      "Difference [  9.580e-04   3.839e-04   2.254e-04   3.839e-04   4.495e-04  -0.000e+00\n",
      "   4.522e-05   0.000e+00   2.612e-04   1.071e-04   3.272e-05   0.000e+00\n",
      "   0.000e+00   3.977e-05   7.051e-06   0.000e+00]\n"
     ]
    }
   ],
   "source": [
    "Vpi=compute_vpi(pis_VI[15], mdp, gamma=GAMMA)\n",
    "V_vi = Vs_VI[15]\n",
    "print(\"From compute_vpi\", Vpi)\n",
    "print(\"From value iteration\", V_vi)\n",
    "print(\"Difference\", Vpi - V_vi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 3b: state-action value function\n",
    "\n",
    "Next, you'll write a function to compute the state-action value function $Q^{\\pi}$, defined as follows\n",
    "\n",
    "$$Q^{\\pi}(s, a) = \\sum_{s'} P(s,a,s')[ R(s,a,s') + \\gamma V^{\\pi}(s')]$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "nbgrader": {
     "grade": false,
     "grade_id": "compute_qpi",
     "locked": false,
     "solution": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[43m\n",
      "Qpi:\n",
      " [[  0.38    3.135   1.14    0.095]\n",
      " [  0.57    3.99    2.09    0.95 ]\n",
      " [  1.52    4.94    3.04    1.9  ]\n",
      " [  2.47    5.795   3.23    2.755]\n",
      " [  3.8     6.935   4.56    0.855]\n",
      " [  4.75    4.75    4.75    4.75 ]\n",
      " [  4.94    8.74    6.46    2.66 ]\n",
      " [  6.65    6.65    6.65    6.65 ]\n",
      " [  7.6    10.735   8.36    4.655]\n",
      " [  7.79   11.59    9.31    5.51 ]\n",
      " [  8.74   12.54   10.26    6.46 ]\n",
      " [ 10.45   10.45   10.45   10.45 ]\n",
      " [ 11.4    11.4    11.4    11.4  ]\n",
      " [ 11.21   12.35   12.73    9.31 ]\n",
      " [ 12.16   13.4    14.48   10.36 ]\n",
      " [ 14.25   14.25   14.25   14.25 ]]\n",
      "\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "def compute_qpi(vpi, mdp,  gamma):\n",
    "    # YOUR CODE HERE\n",
    "    return Qpi\n",
    "\n",
    "begin_grading()\n",
    "Qpi = compute_qpi(np.arange(mdp.nS), mdp, gamma=0.95)\n",
    "print(\"Qpi:\\n\", Qpi)\n",
    "end_grading()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we're ready to run policy iteration!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "nbgrader": {
     "grade": false,
     "locked": false,
     "solution": false
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration | # chg actions | V[0]\n",
      "----------+---------------+---------\n",
      "   0      |      1        | -0.00000\n",
      "   1      |      9        | 0.00000\n",
      "   2      |      2        | 0.39785\n",
      "   3      |      1        | 0.45546\n",
      "   4      |      0        | 0.53118\n",
      "   5      |      0        | 0.53118\n",
      "   6      |      0        | 0.53118\n",
      "   7      |      0        | 0.53118\n",
      "   8      |      0        | 0.53118\n",
      "   9      |      0        | 0.53118\n",
      "  10      |      0        | 0.53118\n",
      "  11      |      0        | 0.53118\n",
      "  12      |      0        | 0.53118\n",
      "  13      |      0        | 0.53118\n",
      "  14      |      0        | 0.53118\n",
      "  15      |      0        | 0.53118\n",
      "  16      |      0        | 0.53118\n",
      "  17      |      0        | 0.53118\n",
      "  18      |      0        | 0.53118\n",
      "  19      |      0        | 0.53118\n"
     ]
    },
    {
     "data": {
      "image/png": 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eCitXwlNPQVWVa8MQEZFZbtatqejudiYQvAoVbS0tZBUXO0ePx7eT7k9JIRaL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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddb0080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def policy_iteration(mdp, gamma, nIt):\n",
    "    Vs = []\n",
    "    pis = []\n",
    "    pi_prev = np.zeros(mdp.nS,dtype='int')\n",
    "    pis.append(pi_prev)\n",
    "    print(\"Iteration | # chg actions | V[0]\")\n",
    "    print(\"----------+---------------+---------\")\n",
    "    for it in range(nIt):        \n",
    "        vpi = compute_vpi(pi_prev, mdp, gamma)\n",
    "        qpi = compute_qpi(vpi, mdp, gamma)\n",
    "        pi = qpi.argmax(axis=1)\n",
    "        print(\"%4i      | %6i        | %6.5f\"%(it, (pi != pi_prev).sum(), vpi[0]))\n",
    "        Vs.append(vpi)\n",
    "        pis.append(pi)\n",
    "        pi_prev = pi\n",
    "    return Vs, pis\n",
    "Vs_PI, pis_PI = policy_iteration(mdp, gamma=0.95, nIt=20)\n",
    "plt.plot(Vs_PI);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compare the convergence of value iteration and policy iteration on several states.\n",
    "For fun, you can try adding modified policy iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NYKbSOB9ntGQAMDhnrkiZ5E1X19KyKCvLGe24/HI4+2y304iIhL6S3iRuL1AD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\nAIsWLWLUqFGsWLGi0Bvs8aSkpNChQwc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fxNX9dSvwCO6vQ9nkPGz/tKR5kg4oOyDrs/1J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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ddbf208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NG2D7diUeIiLpIJ5SvR8DJzvnvqw0urIS0JyDWjjnVOMRB+1KKyKSPuLp8WhJ\nxZ6OqA7AjvqFk97yd+azfdd21XjEKByGUMib1SIiIg1bPInHv4ELy913ZhYCbgTeSkhUaapsnxYN\ntcQkHIbu3SEjw+9IRESkvuIZarkReNPMjgSaA/cCB+P1eBybwNjSjpZLj49mtIiIpI94Non7BDgA\neA94CW/o5QXgCOfcqsSGl160QVx8lHiIiKSPuNbxcM7lOefucs6NdM6d6py71Tm3sT6BmNk4M1tt\nZoVm9oGZHVXLsT81s9fM7BszyzOz+Wb24/pcPxWiPR6q8ag755R4iIikk5iHWsxscG2PO+fejeOc\n5wIPAJcDHwLjgXlmdoBzLreapwwGXgNuBrYClwB/N7MBzrmlsV4/VXILcmndvDUZTVWsUFebNkF+\nvhIPEZF0EU+Nx9vVtLly38ez+9l4YLpzbhaAmV0BnIaXUNxb5WLOja/U9FszOxP4CRDYxENTaWOn\nqbQiIuklnqGW9pVue+ItHPYfvDU+YmJmzYD+wJvRNuecA94AjqnjOQxoDXwb6/VTSYuHxS6aePTq\n5W8cIiKSGDH3eDjn8qppft3MioAH8ZKIWHTC6yXZVKl9E3BgHc9xA16R65wYr51S2qclduEw7LMP\nZGb6HYmIiCRCInenjSVRSBgzOx/4HTCihnqQwMgtyNVQS4xUWCoikl7iKS7tW7kJb6O43wBL4ogh\nFygG9qrUvhfw9W5iOQ94BPiZc65Oi5eNHz+etm3bVmgbNWoUo0aNqnPA8YoURDgu67ikXyedhMNw\nxBF+RyEi0njk5OSQk5NToS0vr7rBjvjEU1y6BK+Y1Cq1f4BXDBoT59xOM1sEDANehrKajWHA1Jqe\nZ2ajgEeBc51z/6zr9SZPnky/fv1iDTMhVOMRm+hU2hEj/I5ERKTxqO6P8cWLF9O/f6yVFNWLJ/Ho\nWel+CRBxzm2vRxwPAjNLE5DodNosYCaAmU0CujrnLiq9f37pY9cA/zGzaG9JoXNuWz3iSJqi4iLy\nduSpxiMGmzdDXp6GWkRE0kk8xaVrEx2Ec26OmXUCJuINsSzB2wE3UnpIZ6BbuadchleQ+lDpLepx\n4uh1SYXNBZsBLZceC02lFRFJP3VKPMzsmrqe0DlX4/DIbp43DZhWw2NjKt0fGs81/KTl0mMXTTyy\ns/2NQ0REEqeuPR6VF+yqiaOWuozGTBvExS4chs6doVUrvyMREZFEqVPi4ZyrXNchMYr2eKjGo+7C\nYfV2iIgKQYsfAAAgAElEQVSkm0Su4yG1yC3IpXmT5rRu3trvUBoMreEhIpJ+4pnVgpntA5wBdAea\nl3/MOXd9AuJKO9GptN5MYamLcBhOP93vKEREJJHiWUAsut7GF8BBwCfAvnjreixOZHDpRBvExWbL\nFm86rXo8RETSSzxDLZOA+51zhwLbgXPwprq+AzybwNjSivZpic2qVd5XJR4iIuklnsSjNzCr9Ptd\nQKZz7nvg98BNiQos3eQW5GoqbQw0lVZEJD3Fk3jk80Ndx0ag/EeD/qSvgZZLj004DB07Qvv2fkci\nIiKJFE9x6QfAccByYC7wgJkdCpxd+phUQzUesdGMFhGR9BRP4nE9EF3S6bbS788FVpY+JpWUuBI2\nF2xWjUcMlHiIiKSnePZq+aLc9/nAFQmNKA1t3b6VYlesoZYYhMNw4ol+RyEiIokWc42HmT1qZkOS\nEEva0nLpsfnuO9i0ST0eIiLpKJ7i0j2Af5rZejO7z8wOS3RQ6UYbxMVGU2lFRNJXzImHc+5MoAtw\nB3AUsNjMPjWzW8xs38SGlx6iPR6q8agbJR4iIukrrr1anHNbnHOPOOeGAD2AmcAFQDhxoaWP3IJc\nDKNDZge/Q2kQwmFo29abTisiIumlXpvEmVkz4EhgIN6y6ZsSEFPaiRRE6JjVkSahJn6H0iBEZ7Ro\nWxsRkfQTV+JhZkPN7K94icZMYBtwOrBP4kJLH1o8LDaaSisikr7i2STuK6AD8E/gcuDvzrkdiQ4s\nnWifltiEw3DssX5HISIiyRDPAmITgGedc1sTHEvayi3I1VTaOioshC+/VI+HiEi6imdWy1+VdMQm\nUqChlrr6onR5OiUeIiLpqV7FpVI3qvGou+iutEo8RETSkxKPJHPOqcYjBuEwtGwJe+3ldyQiIpIM\nSjySrGBnAdt3bVeNRx1pKq2ISHpT4pFkWi49NppKKyKS3pR4JJk2iIuNEg8RkfSmxCPJoj0eqvHY\nvR07YN06JR4iIulMiUeS5RbkAhpqqYs1a6CkRImHiEg6U+KRZJH8CK2btyajaYbfoQSeptKKiKQ/\nJR5JFimIqL6jjsJhaNECunb1OxIREUkWJR5JFsnXGh51FQ5DdjaE9L9SRCRt6Vd8kuUW5qq+o440\no0VEJP0p8UiySL6GWupKiYeISPpT4pFk2iCubnbu9Ga1KPEQEUlvSjySTDUedbNuHezapcRDRCTd\nKfFIop3FO8nbkacejzqITqXNzvY3DhERSS4lHklUtniYajx2KxyGZs2gWze/IxERkWRS4pFE2iCu\n7sJh6NkTmjb1OxIREUkmJR5JFN0gTjUeu6cZLSIijYMSjyTSUEvdKfEQEWkclHgkUaQgQvMmzWnd\nvLXfoQRacTF88YUSDxGRxkCJRxJF8r01PMzM71AC7csvoahIiYeISGOgxCOJIgVaw6MutCutiEjj\nocQjiXILclXfUQfhMDRpAj16+B2JiIgkmxKPJNJy6XUTDntJR/PmfkciIiLJpsQjiaI1HlI7zWgR\nEWk8lHgkkWo86kaJh4hI46HEI0lKXAmbCzarxmM3Skpg1SolHiIijYUSjyTZun0rxa5YQy27sXEj\nFBYq8RARaSyUeCRJdLl09XjUbtUq76sSDxGRxkGJR5JEN4hTjUftwmEw8zaIExGR9KfEI0nK9mnR\nUEutwmHo1g1atPA7EhERSYXAJB5mNs7MVptZoZl9YGZH1XJsZzObbWafmVmxmT2YyljrIpIfwTA6\nZHbwO5RA04wWEZHGpanfAQCY2bnAA8DlwIfAeGCemR3gnMut5ikZwDfAHaXHBk6kIELHrI40CTXx\nO5RAC4fhqBpTTJHgWLduHbm51f06Emn4OnXqRPfu3VNyrUAkHnjJw3Tn3CwAM7sCOA24BLi38sHO\nubWlz8HMfpHCOOsskq81PHbHOS/xGDXK70hEardu3Tp69+5NQUGB36GIJEVWVhbLly9PSfLhe+Jh\nZs2A/sDd0TbnnDOzN4BjfAusnnILc1XfsRuRCHz3nYZaJPhyc3MpKCjgySefpHfv3n6HI5JQy5cv\nZ/To0eTm5jaOxAPoBDQBNlVq3wQcmPpwEiOSH9FU2t3QrrTS0PTu3Zt+/fr5HYZIgxaY4tJ0ow3i\ndi+aePTq5W8cIiKSOkHo8cgFioG9KrXvBXyd6IuNHz+etm3bVmgbNWoUoxJcaKAaj90Lh6FrV2jZ\n0u9IREQkKicnh5ycnApteXl5CTu/74mHc26nmS0ChgEvA5iZld6fmujrTZ48OSVdpbkFqvHYHU2l\nFREJnur+GF+8eDH9+/dPyPl9TzxKPQjMLE1AotNps4CZAGY2CejqnLso+gQzOwwwoBWwR+n9Iufc\n8hTHXkV+UT6FuwpV47Eb4TAceqjfUYiISCoFosbDOTcH+DUwEfgf0Bc42TkXKT2kM9Ct0tP+BywC\n+gHnA4uBV1MS8G5El0tXj0ft1OMhkn5mzpxJKBRi3bp1Kb/2kCFDGDp0aMqvWx/77rsvl1xyid9h\npFQgEg8A59w059y+zrlM59wxzrn/lntsjHPuhErHh5xzTSrdAlGmGN0gTjUeNfv2W9iyRYmHSLox\nM7zRcn+uHQr98LG2ceNGbr/9dj766CNf4olasGABt99+O9u2bavyWCgU8u3n5ZegDLWklbJ9WjTU\nUiNNpRWRRHv99dcr3N+wYQO33347PXv2pG/fvj5FBfPnz2fixImMGTOGNm3aVHjss88+q5AsNQaN\n61+bIhpq2b1o4pGd7W8cIpI+mjZtStOmP/w97ZxLynViXcG2tjiaNWtGkyaNa2sNJR5JEMmP0Lp5\nazKaZvgdSmCFw7DnnlAp+ReRFHr++ecJhUL8+9//rvLY9OnTCYVCLFu2DICPP/6YMWPGkJ2dTWZm\nJl26dOEXv/gF33777W6vEwqFmDhxYpX26uob8vLyuO666+jevTstWrRg//335957761TEjFkyBBO\nOMEblX/nnXcYMGAAZsbFF19MKBSiSZMmzJo1q+z4hQsXMnz4cNq1a0fLli0ZMmQI8+fPr3DOCRMm\nEAqFWL58Oeeffz4dOnRg0KBBdf6Z3H777dx4441l/95oHNEamOp+BqtXr2bEiBF07NiRli1bcswx\nxzB37twKx7zzzjuEQiGeffZZ7rrrLrp160ZmZiYnnngiq1at2u3Pyk8aakmCSIHW8NgdFZaK+O+0\n006jVatWzJkzp+zDNGrOnDkccsgh9OnTB/CGMVavXs0ll1xC586d+fTTT5k+fTrLli1jwYIFcV2/\ncm1DYWEhgwcPZuPGjVxxxRV069aN+fPnc/PNN/P111/z4IO1b0Re/ny9e/dm4sSJ/P73v2fs2LFl\n/74f/ehHAPzrX//i1FNP5cgjjyxLLmbMmMEJJ5zAe++9x5FHHlnhnCNGjOCAAw5g0qRJZUlQXX4m\n55xzDp9//jlPP/00U6ZMoWPHjgDsscce1f4MvvnmG4455hi2b9/OtddeS4cOHXj88cc544wzeP75\n5znzzDMrHH/PPffQpEkTbrjhBvLy8vjDH/7A6NGj435NUkGJRxLkFuSqvmM3wmHYf3+/oxBJjoIC\nWLEiudc46CDIyqrfOVq0aMFPfvITnnvuOaZOnVr2Ibhp0ybeeeedCr0U48aN4/rrr6/w/IEDB3L+\n+efz/vvvc+yxx9YvGOCBBx5g9erVLFmyhF6lSxpfdtlldOnShfvvv59f/epX7L333nU615577skp\np5zC73//e4455hjOP//8Co9feeWVDBs2jFdf/WEy5NixY+nTpw+33nor//znPyscf8QRR/DEE09U\naKvLz+SQQw6hX79+PP3005x55pm73Qtl0qRJRCIR3nvvPY45xtuu7NJLL6Vv375cf/31VRKPHTt2\nsHTp0rLhmnbt2nHdddexbNmysqQxaJR4JIGWS9+9cBhOOcXvKESSY8UKSNBaSzVatAgSsRbiueee\ny9NPP83bb79dNhX12WefxTnHyJEjy47LyPhh6HjHjh18//33DBw4EOccixcvTkji8dxzzzFo0CDa\ntm3L5s2by9qHDRvGPffcw7vvvpuQVaaXLFnCypUr+d3vflfhOs45hg0bxpNPPlnheDNj7NixVc6T\njJ/JP/7xDwYMGFCWdAC0bNmSyy+/nFtuuaVKQnHJJZdUqBEZNGgQzjm++OILJR6NSSQ/woGdGuz+\ndkmXl+ftTKvCUklXBx3kJQbJvkYiDB8+nDZt2vDMM8+UJR5z5szh8MMPZ79y46FbtmxhwoQJPPPM\nM3zzzTdl7WaWsOW0V65cyccff1w2DFGemVW4bn2vA3DhhRdW+3goFCIvL6/C9ho9e/asclwyfiZr\n167l6KOPrtIe3RV57dq1FRKKbt0qLnHVvn37stiCSolHEkQKIhybWf/sP11F655U4yHpKisrMb0R\nqdC8eXPOOussXnzxRaZNm8bGjRt5//33ueeeeyocN2LECD744ANuvPFGDjvsMFq1akVJSQknn3wy\nJSUlcV27uLi4wv2SkhJOOukkbrrppmqLSQ844IC4rlNZNN4HHniAww47rNpjWrVqVeF+ZmZmlWOS\n8TOJVU0zYpI1oycRlHgkgWo8aqc1PESC5dxzz2XWrFm8+eabfPrppwAVhlm2bt3Kv/71L+644w5+\n+9vflrWHo2/m3Wjfvj1bt26t0LZz5042btxYoS07O5vvv/8+YauP1rQwV3Zpd2vr1q3LZsHEKpaf\nSSwLhPXo0YPPPvusSvvy5cvLHm/oNJ02wXYW72Tr9q2q8ahFOAzt20OHDn5HIiIAJ554Iu3bt+fp\np59mzpw5DBgwoMIHXPSv6sp/xU+ePLlOH6rZ2dm8++67FdqmT59epcdj5MiRLFiwgNdee63KOfLy\n8qocvzstS7e+rpz09O/fn+zsbO6//37y8/OrPC83N3e3547lZ1JTHNU59dRT+fDDD1m4cGFZW35+\nPo888gg9e/YMbN1GLNTjkWBatXT3NJVWJFiaNm3K2WefzdNPP01BQQEPPPBAhcdbt27N4MGDuffe\neykqKmLvvffmtddeY82aNXXq0r/00ku54oor+NnPfsZJJ53E0qVLee2116rUctxwww28/PLLnH76\n6Vx88cX079+f/Px8PvroI1544QXWrFlDhxj+YsnOzqZdu3b85S9/oVWrVrRs2ZKBAwey77778uij\nj3Lqqady8MEHM2bMGPbee2+++uor3nrrLdq2bctLL71U67lj+Zn0798f5xy33HIL5513Hs2aNeOM\nM86odvjmN7/5DTk5OQwfPpxrrrmGDh06MHPmTNauXcsLL7xQ5397kCnxSLDoqqVax6NmSjxEgufc\nc8/lb3/7G6FQiBEjRlR5PCcnh6uvvppp06bhnOPkk0/mH//4B127dt1tr8dll13GmjVr+Nvf/sa8\nefMYPHgwr7/+OsOGDavw3MzMTN59913uvvtunn32WZ544gnatGnDAQccwMSJEysUe9ak/PmaNm3K\nrFmzuPnmm7nyyivZtWsXM2bMYN999+X4449nwYIF3HHHHTz00EN8//33dO7cmYEDB1Y7g6U6df2Z\nHHnkkdx555385S9/Yd68eZSUlLB69Wq6d+9eZW+bPffckwULFnDTTTfx5z//me3bt9O3b19eeeUV\nhg8fXuO/tS7tQWFBLkBJJDPrByxatGgR/ZJY9fWv1f9i2KxhhK8Ok91B0zaq07UrXHopVLOQoUgg\nLV68mP79+5Ps3x8ifqjL/+/oMUB/59zi+lxPNR4JFt2ZVkMt1cvPh40b1eMhItJYKfFIsEhBhOZN\nmtO6eWu/QwkkTaUVEWnclHgkWCTf26cl6GNsftFUWhGRxk2JR4LlFuRqKm0twmFo3RqqWZhQREQa\nASUeCRYpiKi+oxbRGS3qEBIRaZyUeCSYNoirnabSiog0bko8Eixa4yHVU+IhItK4KfFIMNV41Kyw\nENavV+IhItKYKfFIoBJXog3iarF6tfdViYeISOOlxCOBtm7fSrErVo9HDbSGh4iIKPFIoOiqparx\nqF44DJmZ0KWL35GIiIhflHgkkHamrZ2m0oo0DkOGDOGEE04ou7927VpCoRCzZs1KWQzvvPMOoVCI\nd999N2XXrK+ZM2cSCoVYt26d36EklRKPBIruTKuhluppRotI41Ddys1+rOZc+Zo5OTlMmTIl5XFU\nNmnSJF566aUq7ZV3qk1XSjwSKJIfwTA6ZHbwO5RAUuIh0jj16NGDwsJCLrjggpRd8/jjj6ewsJDB\ngweXtT311FOBSDzuvvvuahOPCy+8kMLCQrp37+5DVKmjxCOBIgUROmR2oEmoid+hBE5REaxZo8RD\npLFq3rx5yv+ab968edKv4Zxjx44dCTmXmaUkZr8p8UggTaWt2dq1UFKixEMkaCZMmEAoFOKzzz5j\n5MiRtG3blk6dOnHddddV+UAtLi7mjjvuYL/99qNFixb07NmT3/72txQVFdV6jZpqPKLX3HPPPcnK\nyuKggw7i1ltvBeDtt98mFApV2zPw1FNPEQqFWLhwYY3XrFzjMXToUF599dWyWEKhEL169So7vqio\niNtuu43999+fFi1a0L17d2666aYq/7ZQKMQ111zDU089xSGHHEKLFi2YN28eAPfffz/HHnssnTp1\nIisriyOPPJLnn3++yvMLCgrK6jlCoRCXXHIJUHONx7Rp08qutffee3PVVVeRl5dX4ZghQ4bQt29f\nli9fztChQ2nZsiX77LMP9913X40/I7809TuAdKLl0mumXWlFginaCzFy5Eh69uzJPffcwwcffMDU\nqVPZunUrM2fOLDv2F7/4BbNmzWLkyJH8+te/ZuHChUyaNIkVK1ZU+YDdnY8++ohBgwaRkZHB2LFj\n6dGjB6tWreKVV17hzjvvZMiQIXTr1o3Zs2dz5plnVnju7Nmz2W+//Rg4cGCd/m0At956K3l5eXz1\n1Vf88Y9/xDlHq1atAK/X4ic/+Qnz589n7NixHHTQQXz88cdMnjyZlStX8sILL1Q475tvvsmcOXO4\n6qqr6NSpE/vuuy8AU6dO5cwzz2T06NEUFRXx9NNPM3LkSF555RVOOeUUAJ588kl+8YtfMHDgQC6/\n/HIAsrOzy+Kt3Cs0YcIEJk6cyI9//GN++ctf8tlnnzFt2jT++9//8v7779OkSZOy53777beccsop\nnH322Zx33nk899xz/OY3v6Fv376cfPLJsbw8yeWcaxQ3oB/gFi1a5JLl5CdOdmc/c3bSzt+QTZ3q\nXEaGc8XFfkciErtFixa5ZP/+8MuECROcmbmf/vSnFdrHjRvnQqGQ+/jjj51zzi1dutSZmRs7dmyF\n42644QYXCoXc22+/XdY2ZMgQN3To0LL7a9ascWbmHn/88bK2wYMHu7Zt27ovv/yyxthuueUWl5mZ\n6bZt21bWFolEXLNmzdzEiRNr/Xe9/fbbLhQKuXfeeaes7fTTT3c9e/ascuwTTzzhmjZt6ubPn1+h\nffr06S4UCrkFCxaUtZmZa9q0qVuxYkWV82zfvr3C/V27drlDDz3UnXjiiRXaW7Vq5caMGVPl+TNn\nznShUMitXbu27N+akZHhTjnllArHPfTQQy4UCrmZM2eWtQ0ZMsSFQiE3e/bssraioiLXpUsXN2LE\niCrXKq8u/7+jxwD9XD0/j9XjkUCRggg92vbwO4xACoehVy8IaXBPGoGCnQWsyF2R1Gsc1Okgsppl\nJeRcZsa4ceMqtF199dVMmzaNuXPncsghh/Dqq69iZowfP77Ccb/61a+4//77efXVVzn++OPrdL3c\n3Fz+/e9/M378ePbee+8aj7vwwguZNGkSzz33HGPGjAHg6aefpri4mJ///Ocx/itr9txzz9G7d28O\nOOAANm/eXNY+dOhQnHO89dZbHH300WXtQ4YM4cADD6xynoyMjLLvt27dyq5duxg0aBBPP/10XHG9\n8cYb7Ny5k+uuu65C+2WXXcYtt9zCq6++ykUXXVTW3qpVK84///yy+82aNWPAgAF88cUXcV0/WZR4\nJJBqPGqmGS3SmKzIXUH/R/on9RqLLl9Evy79Ena+/Sq9QbOzswmFQqxZswaAdevWEQqFqhy31157\n0a5dO9auXVvna0U/CA8++OBajzvwwAM56qijmD17dlni8dRTT3H00UdXqM+or5UrV7JixQr22KPq\n728z45tvvqnQFh1aqeyVV17hrrvuYsmSJRXqY0Jx/sUV/ZkecMABFdqbNWtGr169qvzM99lnnyrn\naN++PR9//HFc108WJR4JFMlXjUdNwmE47TS/oxBJjYM6HcSiyxcl/RrJVNMMlFTPTLnwwgu57rrr\n2LBhA4WFhXzwwQdMmzYtodcoKSnh0EMPZfLkydGh+Qq6detW4X5mZmaVY/79739z5plnMmTIEB5+\n+GG6dOlCs2bNeOyxx8jJyUlovDWJ1ntUVt2/yU9KPBIkvyifwl2F6vGoxq5d3gZx6vGQxiKrWVZC\neyNSYeXKlfTo8cNQcTgcpqSkhJ49ewL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61mVvAu8Co7Xe3e3x6izHbcD5wMfA68AHNHtH\nJJ2mfOdSSZLUGWc8JElSZwwekiSpMwYPSZLUGYOHJEnqjMFDkiR1xuAhSZI6Y/CQJEmdMXhIkqTO\nGDwkSVJnDB6SJKkzBg9JktQZg4ckSerMX2M8D1fqf7mZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113332748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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652bGML5AihRE6N2xd8M7tiDliYeGWkREpD5NTjyAnwJXOecWVNr2rJl9hHc5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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11337e128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UeNQzVS2NjZbSioikhpgTDzM7wMxONrPMkvsaO6gF7UwbGyUeIiKpIZa9WtqY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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1133dd438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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67zgl26VINLV4pKc7rR2q3SEiEn78quNhjBlljFkP7Af2G2PWFS0aJy4oKCwg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\ncJ0DBw6UeX3o0CF78skn23PPPbfM9qS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CGlO+S9JmUiXp35NqMT1bQrjWg+7OZ37NB54i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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11352f7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for s in range(5):\n",
    "    plt.figure()\n",
    "    plt.plot(np.array(Vs_VI)[:,s])\n",
    "    plt.plot(np.array(Vs_PI)[:,s])\n",
    "    plt.ylabel(\"value of state %i\"%s)\n",
    "    plt.xlabel(\"iteration\")\n",
    "    plt.legend([\"value iteration\", \"policy iteration\"], loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Create Assignment",
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
